It seems Einstein's equivalence principle is neglecting time dilation. If an observer is at rest in an inertial reference frame, free of any gravitation, she will experience time flow at the "native" rate of a universe empty of mass and energy. However, an observer in free fall at the surface of the earth will experience time flow at a rate determined by earth's gravitation, which is slower than the native time flow rate. This seems to imply non-equivalence?
Not only is the equivalence principle not ignoring time dilation, you can actually use the equivalence principle to derive gravitational time dilation.
The issue that you are running into is probably the most common issue in applying the equivalence principle. That is that the equivalence principle is strictly local. It cannot be applied over a region of spacetime which is large enough for tidal effects (spacetime curvature) to be noticed. The comparison of the free faller with some distant clock is a non-local comparison and the equivalence principle makes no claim about the outcome.